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Einstein Metrics on Complex Surfaces

Claude LeBrun
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Abstract

We consider compact complex surfaces with Hermitian metrics which are Einstein but not Kaehler. It is shown that the manifold must be CP2 blown up at 1,2, or 3 points, and the isometry group of the metric must contain a 2-torus. Thus the Page metric on CP2#(-CP2) is almost the only metric of this type.

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BibTeXRIS

Claude LeBrun. 1995-06-29. Einstein Metrics on Complex Surfaces. https://arxiv.org/abs/dg-ga/9506012

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